Edits

• 09/17/24:
  • Changed q634 and q635 for the ratio, and took out the original variables (including a missing dummy).
  • Took out “Business situation” from predicting models.
  • Tested taking out “cluster” variable for entire sample prediction/ taking out definition of success variables.
  • Added a love plot beside varImp plots.
• 09/18/24:
  • Changed max and min income to a ratio with respect to assets in their first loan.
  • Fix 5 obs that had missing ratio (both q634 and q635 were 0).
  • Added preliminary code for selecting 10 variables.
• 09/26/24:
  • Imputed missing survey age (148) with admin data
  • Changed max and min income to logarithms (to treat outliers) and avoid high means for standardization.
  • Checked ratio of resources needed and increase of income (transformed to logs)
• 10/03/24:
  • Changed max and min income to percentile (1-100).
  • Changed ratio of investment and income growth to percentile (1-100), and also added the amount of the investment as a variable.
  • Included cluster variable in the model selection.
• 10/14/24:
  • Multiple iterations of RFE for variable selection (05b_rfe_for_variable_selection.R)
  • Comparison between average business and business predicted as successful.

Definition of Success

In this section, we analyze the characteristics of clients according to their definition of success. We will use the following questions to build definitions of success in a data-driven way:

1. Why do you consider yourself a successful person? (Open)

2. For you, a successful person is mainly someone who:

• Is recognized by the community.
• Has stability at home.
• Has stability in their business.

3. For you, a successful business is if:

• It has managed to grow.
• It has manages to maintain itself.
• It has generated employment.
• It has generated a positive change in the community.
• It allows me to cover household necessities.

4. Imagine that everything goes well, what would be the size of your business in 5 years?

• Smaller/the same as now.
• Larger than now.
• Much larger than now.

5. Imagine that everything goes well, how many people would work in your business in 5 years? (% growth)

6. If the opportunity presented itself to work in a company with a permanent company, what would you do?

• Sell my current business/ Close my current business if I can’t sell it.
• Keep my current business (in parallel or managed by another person).
• Wouldn’t accept it.

7. What amount of money would you accept for a job? (1,000 US$)

8. You would like that your children:

• Were entrepreneurs and had their own business.
• Managed the family business.
• Had a secure job.

Defining Success

Using the previous questions, we perform a hierarchical clustering analysis (HCA) to obtain optimal clusters based on the customers’ responses. Based on the responses, we create two different clusters to assess differences in definitions of success. To increase the disparity between both groups, we exclude observations that are in the 10% closer to the other cluster’s center, dropping 184 out of 1833 total observations.

The following table shows the comparison between both clusters in terms of the previous data:

Table 1. Balance table across clients’ responses according to clusters

	Cluster 1 (N=1188)		Cluster 2 (N=461)
	Mean	Std. Dev.	Mean	Std. Dev.	Diff. in Means	p
What makes you successful? - business	0.121	0.327	0.158	0.365	0.037	0.057
What makes you successful? - family	0.024	0.152	0.000	0.000	-0.024	0.000
A successful person: Is recognized by the community	0.200	0.400	0.007	0.080	-0.194	0.000
A successful person: Has stability in her home	0.383	0.486	0.449	0.498	0.066	0.015
A successful person: Has stability in her business	0.417	0.493	0.544	0.499	0.128	0.000
A successful business: Has managed to grow	0.355	0.479	0.360	0.481	0.005	0.853
A successful business: Has managed to sustain	0.216	0.412	0.260	0.439	0.044	0.064
A successful business: Has generated employment	0.136	0.343	0.174	0.379	0.037	0.067
A successful business: Has brought about a positive change in the community	0.102	0.303	0.000	0.000	-0.102	0.000
A successful business: Covers the household needs	0.190	0.393	0.206	0.405	0.016	0.472
Business would be much larger	0.608	0.488	0.577	0.495	-0.031	0.256
Business would be larger	0.000	0.000	0.000	0.000	0.000
Business would be equal/smaller	0.392	0.488	0.423	0.495	0.031	0.256
How many workers would you have? (prop. over current workers)	3.421	3.515	3.579	4.152	0.157	0.472
If offered a job: Accept and keep	0.788	0.409	0.061	0.239	-0.727	0.000
If offered a job: Close or sell	0.000	0.000	0.000	0.000	0.000
If offered a job: Not accept	0.212	0.409	0.939	0.239	0.727	0.000
What amount of money would a job have to pay? (1,000 US$)	5.187	5.439	11.976	0.535	6.789	0.000
What amount of money would a job have to pay? (No amount)	0.385	0.487	0.998	0.047	0.613	0.000
You would like your children: Were entrepreneurs and had their own business	0.573	0.495	0.644	0.479	0.071	0.008
You would like your children: Took charge of the family business (their business)	0.238	0.426	0.356	0.479	0.118	0.000
You would like your children: Had a secure job	0.189	0.391	0.000	0.000	-0.189	0.000

The following plot shows the relative importance of the previous variables in terms of the difference between clusters measured in standard deviations. Negative differences imply a higher value for cluster 2 and positive differences imply a higher value for cluster 1.

Figure 1. Variable Importance in Cluster Formation

Characteristics by cluster

In this section, we compare different characteristics by clusters, as previously defined. We can see that clients in Cluster 2 have better loan characteristics and business performance, but they have otherwise similar characteristics in terms of risk and loss aversion and investment decisions. Surprisingly, individuals in Cluster 2 have lower education compared to Cluster 1, and are more likely to be the main providers for their households.

Balancing Business Performance

We are also interested in analyzing whether the definitions of success for each individual are mainly mediated by the performance of their own business. For that reason, we match observations in Cluster 2 to Cluster 1 to balance the means of business’ performance with a tolerance of 0.025 SD. We are able to match 100% of the observations in Cluster 2, obtaining the following pre- and post-matching differences:

Analyzing now the differences between the matched observations, we can see that there are still significant differences between Cluster 1 and Cluster 2 in terms of their perspectives on success, even after adjusting by business performance:

Analyzing potential differences in other outcomes, we obtain the following results after matching:

Prediction of Success

We are interested in using the information available to see which characteristics would be good predictors of success, especially depending on the definition of success the individual has. For this, we will use two different definitions of success: (i) Loan growth and timely payments, and (ii) Success score.

The first measure, which was used for stratification purposes for sampling our survey population, identifies clients who have had growth in terms of loan amount (between their first and last registered loan), as well as overall timely payments. The second measure identifies micro-entrepreneurs that belong to the top quartile of a success score built on their (standardized) growth in terms of assets and loan amount.

Measure 1: Loan growth and timely payments

For the entire sample of individuals that currently own a business and that had more than one loan, we observe that 51.9% is classified as successful (out of individuals). In terms of this measure of success based on their previous definition of success (community/family vs business oriented), we can see that this is balanced between groups, with a slight advantage for Cluster 2 (business oriented) in terms of success.

For predicting the success for the entire sample (only including individuals that currently have a business and that had more than one loan), we use xgboost as the prediction model. We find that accuracy is low, with an average accuracy rate of 54.8%.

Figure 2. Variable importance for success variable prediction - Entire sample

When we look at the different groups by their definition of success, we get an accuracy rate of 47.9% for Cluster 1.

Figure 3. Variable importance for success variable prediction - Community/family oriented group (Cluster 1)

When we look at the different groups by their definition of success, we get an accuracy rate of 48.3% for Cluster 2.

Figure 4. Variable importance for success variable prediction - Business oriented group (Cluster 2)

Measure 2: Success score

We define success score as:

\[Score \ Success_i = \frac{1}{3}(\Delta Loan Amount_i + \Delta Assets_i + \Delta Surplus_i)\]

where \(\Delta X\) represents the change between the last available loan and the first one. All variables are standardized, so they are comparable. If an individual is missing one of these variables, then the weight is re-distributed between the available data. In this case, we are predicting the probability of being in the top 25% of this score. In terms of our previous definitions of success, individuals that have a business-oriented definition of success are more likely to be in the top 25% (30.7%) compared to the community/family-oriented cluster (23%).

Using the same xgboost method as for the previous measure, we have an accuracy in prediction of 74.3% for the entire sample.

Figure 5. Variable importance for Top 25% of Success Score prediction - Entire sample

Figure 6. ROC - Entire Sample

We can also analyze the partial change in probabilities for some of the predictors that are deemed some of the most important in the data:

Figure 7. Partial dependence between Top 25% Success and top predictors of full model

Figure 8. Partial dependence between Top 25% Success and top predictors of full model for Growth and Investment

For the group that has a community/family vision of success, we have an accuracy in prediction of 73.5%.

Figure 9. Variable importance for Top 25% of Success Score prediction - Community/Family oriented group (Cluster 1)

Figure 10. ROC - Community/Family oriented group (Cluster 1)

For the group that has a business-like definition of success, we have an accuracy in prediction of 66.7%.

Figure 11. Variable importance for Top 25% of Success Score prediction - Business oriented group (Cluster 2)

Figure 12. ROC - Business oriented group (Cluster 2)

Variable selection

We would like to select the most predictive covariates in our survey (up to 15 features) to reduce the dimensionality of the instrument. For this, we use Recursive Feature Elimination in combination with Random Forest to select models with 5, 7, 10, and 15 features. Each model is fitted independitly (so they are not necessarily nested), and for 10 iterations to find the top variables. In this case, the selected model has 7 variables, with an accuracy of 74.4% in the testing data. The selected features are the following:

We can also plot the partial dependence between the outcome variable and the top 4 features. This would give us an idea of how the probability of being assigned to each class changes through the range of values of the predictor, holding other variables constant.

Figure 13. Partial dependence between Top 25% Success Score and most relevant predictors